You can use Fixie with any HTTP library. Popular options include Apache HttpClient and OkHttp.

Using HttpClient

import org.apache.http.HttpHost;
import org.apache.http.auth.AuthScope;
import org.apache.http.auth.UsernamePasswordCredentials;
import org.apache.http.client.CredentialsProvider;
import org.apache.http.client.config.RequestConfig;
import org.apache.http.client.methods.CloseableHttpResponse;
import org.apache.http.client.methods.HttpGet;
import org.apache.http.impl.client.BasicCredentialsProvider;
import org.apache.http.impl.client.CloseableHttpClient;
import org.apache.http.impl.client.HttpClients;
import org.apache.http.util.EntityUtils;

public class FixieExample
{
    public static void main(String[] args) throws Exception {
        String fixieUrl = System.getenv("FIXIE_URL");

        String[] fixieValues = fixieUrl.split("[/(:\\/@)/]+");
        String fixieUser = fixieValues[1];
        String fixiePassword = fixieValues[2];
        String fixieHost = fixieValues[3];
        int fixiePort = Integer.parseInt(fixieValues[4]);

        CredentialsProvider credsProvider = new BasicCredentialsProvider();
        credsProvider.setCredentials(
                new AuthScope(fixieHost, fixiePort),
                new UsernamePasswordCredentials(fixieUser, fixiePassword));
        CloseableHttpClient httpclient = HttpClients.custom()
                .setDefaultCredentialsProvider(credsProvider).build();
        try {
            HttpHost proxy = new HttpHost(fixieHost, fixiePort);
            RequestConfig config = RequestConfig.custom()
                .setProxy(proxy)
                .build();

            HttpHost target = new HttpHost("www.example.com", 80, "http");
            HttpGet httpget = new HttpGet("/");
            httpget.setConfig(config);

            CloseableHttpResponse response = httpclient.execute(target, httpget);
            try {
                System.out.println(EntityUtils.toString(response.getEntity()));
            } finally {
                response.close();
            }
        } finally {
            httpclient.close();
        }
    }
}

Using OkHttp

import java.io.IOException;
import java.net.InetSocketAddress;
import java.net.Proxy;
import okhttp3.OkHttpClient;
import okhttp3.Authenticator;
import okhttp3.Credentials;
import okhttp3.MediaType;
import okhttp3.Request;
import okhttp3.RequestBody;
import okhttp3.Response;
import okhttp3.Route;

public class FixieExample
{
    public static void main(String[] args) throws Exception {
        String fixieUrl = System.getenv("FIXIE_URL");
        String[] fixieValues = fixieUrl.split("[/(:\\/@)/]+");
        String fixieUser = fixieValues[1];
        String fixiePassword = fixieValues[2];
        String fixieHost = fixieValues[3];
        int fixiePort = Integer.parseInt(fixieValues[4]);

        OkHttpClient.Builder clientBuilder = new OkHttpClient.Builder();
        Authenticator proxyAuthenticator = new Authenticator() {
          @Override public Request authenticate(Route route, Response response) throws IOException {
               String credential = Credentials.basic(fixieUser, fixiePassword);
               return response.request().newBuilder()
                   .header("Proxy-Authorization", credential)
                   .build();
          }
        };
        clientBuilder.proxy(new Proxy(Proxy.Type.HTTP, new InetSocketAddress(fixieHost, fixiePort)))
        .proxyAuthenticator(proxyAuthenticator);

        OkHttpClient client = clientBuilder.build();
        Request request = new Request.Builder().url("http://www.example.com").build();
        Response response = client.newCall(request).execute();

        System.out.println(response.body().string());
    }
}

Using java.net.ProxySelector

Java supports a system property socksProxyHost, which can be used to route every outbound request through Fixie Socks. Additionally, Java 7 introduced ProxySelector, which can be used to conditionally proxy requests depending on the hostname.

A simple example that proxies all outbound requests through Fixie Socks:

URL fixie = new URL(System.getenv("FIXIE_SOCKS_HOST"));
String[] fixieUserInfo = fixie.getUserInfo().split(':');
String fixieUser = fixieUserInfo[0];
String fixiePassword = fixieUserInfo[1];
System.setProperty("socksProxyHost", fixie.getHost());
Authenticator.setDefault(new ProxyAuthenticator(fixieUser, fixiePassword));

//...

private class ProxyAuthenticator extends Authenticator {
  private final PasswordAuthentication passwordAuthentication;
  private ProxyAuthenticator(String user, String password) {
    passwordAuthentication = new PasswordAuthentication(user, password.toCharArray());
  }

  @Override
  protected PasswordAuthentication getPasswordAuthentication() {
    return passwordAuthentication;
  }
}